m Solve the eqution to find the complex roots z"- -1ti @find the qubic roots of (-27i) Hiw 3. -27; {

Q: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: (i) Evaluate the complex number (a+bi)4n+2 + (b − ai) 4n+2 where n is any positive integer. (ii)…

A: This is a problem of complex analysis.

Q: 4. Find all solutions in the complex numbers to the following equations. (a) z5 = z. (b) 24 = iz².

A:

Q: What is the nature of the roots of 2y"+24y+72? O Complex conjugate O None of the above Distinct…

A: Given equation is . Let us denoted it by Now, on compare above equation with We get,

Q: Find all solutions of the following equationsa a)z/1-z=1-5i   b) (2-i)z+8z^2=0.  c)z^4-16=0

A: a). z1-z = 1 - 5i⇒ z = (1-5i)(1-z)⇒ z = 1 - z - 5i + 5iz⇒ (2 - 5i)z = 1-5i⇒ z = 1-5i2-5i

Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: Use the value of the discriminant, b² - 4ac, to determine the number and type of roots for x²-3x+7=0…

A: We have to use the value of the discriminant, b²-4ac, to determine the number and type of roots for…

Q: 4 Get all the roots of 2(V3i – 1) |

A:

Q: Find all complex fourth roots of - 2 + 2/3 i. In other words, find all complex solutions of X x* = -…

A: Given: -2+23i

Q: Let the b and c randomly chosen numbers from interval [-A,A]. Determine the probability that the…

A: It is given that  and  are randomly chosen number on the interval The quadratic equation is

Q: 1. Solve the following equations. a) (7+2/)+(4-3) b) (5-2/ (2-)(4+2) d) 2- 1+2 e) 21-3 2. Find x in…

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Q: Q3) Find complex root of the z³ = -27, k = 0,1

A:

Q: Find all the roots of z = -4 + (4V3)i giving each root in the form re". %3D 8° = -4+ (43) C

A:

Q: Q4/ Solve the equation 0 = iz2 + 2z -i where z is a complex number? %3D

A:

Q: 7. Express the complex number 1/(1+ jV3) in the form Aejº

A:

Q: 3) Find all the roots of the following equations z = √1-i 14 b) c) Z - i z = z = 964

A: a)

Q: What is the 4th roots of z=1+i

A:

Q: 6. Write the complex number is standard form (a + bi) 14- V-98 -7

A: As we know from the radical rule: -a=-1a   Given: 14--98-7

Q: 1 30 (A) = 2 -2 4 3 50 a) Find the minor of the element 5 and 0? b) Find the cofactor of the element…

A: To find the minor and cofactor of element  0 and 5 .

Q: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number z.what is…

A: Given: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number…

Q: Q4-Find the complex roots of (4 + 4i)ō * (4 + 4i) (Demoivere's formula)

A: given

Q: a

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Q: 1. What are the roots of the equation (x + 1)(4x – 3) = 0? C) x= 1, - D) x= 1 A) x = -1,3 B) x= -1,

A: (x+1)(4x-3)=0⇒(x+1)=0 or (4x-3)=0⇒x=-1 or 4x=3⇒x=-1 or x=34⇒x=-1 ,34

Q: 5. Find all the roots in both polar and Cartesian form for each expression. (a) (-2+2i) *. (b) (-1)…

A: